Finite Group Databasebeta

← C2×#10594296 #11900970

Subgroups — C2×#10594296 #11900970

Order 1152.

4305 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#886C211yesmaximal, characteristic, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×#63922C212yesmaximal, complemented
9C2×#63916C212yesmaximal, complemented
10C2×#63912C212yesmaximal, complemented
11C2×#63854C212yesmaximal, complemented
12#10594296C2116yesmaximal, direct product factor
13C2×#5653—31nomaximal
14C2×#5589—31nomaximal
15C24×C3⋊D3C2211yescharacteristic
16C24×C3×D3C2211yescharacteristic, complemented
17C23×D32C2211yescharacteristic, complemented
18C22×C4×C3⋊D3C2212yescomplemented
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic, complemented
22C22×C3×D12C2212yescomplemented
23C2×#3811—28no—
24C2×#3811C2218yescomplemented
25C22×#626—28no—
26C22×#626C2212yes—
27C22×#626C2212yescomplemented
28C22×#626C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic, complemented
30C22×#626C2218yescomplemented
31C22×#625C2212yescomplemented
32C22×#624C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2211yescharacteristic, complemented
34C2×#3757C2211yescharacteristic, complemented
35C2×#3752C2212yescomplemented
36C22⋊C4×C3⋊D3C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×C4⋊Dic3C2212yescomplemented
40C3×#886C2218yescomplemented
41C3×#882C2218yescomplemented
42#63976C2218yescomplemented
43C2×#3724C2212yescomplemented
44#63961C2218yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46C2×(C2×D3)⋊Dic3C2212yescomplemented
47#63922C22116yescomplemented
48#63916C22116yescomplemented
49#63912C22116yescomplemented
50#63854C22116yescomplemented
51C23×#67—31no—
52C22×D3×D4—31no—
53C22×D3×D4—31no—
54C23×D12—31no—
55C2×C3×#123—31no—
56C2×C3×#120—31no—
57C2×#953—31no—
58C2×#938—32no—
59C2×#937—31no—
60C2×#937—32no—
61C2×#935—31no—
62C2×#929—31no—
63#5653—316no—
64#5589—316no—
65C2×#895—32no—
66C2×#894—32no—
67C2×#886D311yescharacteristic, complemented
68C2×#884—32no—
69C2×#884—32no—
70C2×#883—32no—
71C2×#882—32no—
72C2×#882D311yescharacteristic, complemented
73C2×D3×C22⋊C4—31no—
74C2×D3×C22⋊C4—31no—
75C2×D3×C22⋊C4—61no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3—44no—
78C23×C3⋊D3D418yescomplemented
79C23×C3⋊D3C2311yescharacteristic
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2314yes—
82C23×C3×D3—24no—
83C23×C3×D3—44no—
84C23×C3×D3C2311yescharacteristic
85C23×C3×D3C2312yes—
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2314yescomplemented
88C22×D32—24no—
89C22×D32—44no—
90C22×D32C2314yescomplemented
91C22×C32×C4C2312yes—
92C22×C3⋊Dic3C2312yes—
93C2×C4×C3⋊D3—44no—
94C2×C4×C3⋊D3C2318yescomplemented
95C2×C3×#67—24no—
96C2×C3×#67—24no—
97C2×C3×#67C2314yes—
98C2×C3×#67C2314yes—
99C22×C3×Dic3—24no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2312yes—
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2314yescomplemented
104C2×C3×D12—44no—
105C2×C3×D12C2318yescomplemented
106#3811—232no—
107C2×#626—28no—
108C2×#626—28no—
109C2×#626—24no—
110C2×#626—24no—
111C2×#626—232no—
112C2×#626C2318yes—
113C2×#626C2318yescomplemented
114C2×#626C2314yescomplemented
115C2×#626C2314yescomplemented
116C2×#625—44no—
117C2×#625C2318yescomplemented
118C2×#624—24no—
119C2×#624C2314yescomplemented
120C32×C22⋊C4C2314yescomplemented
121#3757C2314yescomplemented
122#3752C2318yescomplemented
123C3×(C2×D3)⋊C4C2318yescomplemented
124C3×(C2×D3)⋊C4C2318yescomplemented
125C3×C4⋊Dic3C2318yescomplemented
126#3724C2318yescomplemented
127(C2×D3)⋊Dic3C2318yescomplemented
128(C2×D3)⋊Dic3C2318yescomplemented
129C2×#534—91noSylow
130C25×C3—31no—
131C24×D3—31no—
132C24×D3—31no—
133C24×D3—31no—
134C24×D3—31no—
135C24×D3—61no—
136C24×D3C2×D311yescharacteristic, complemented
137C22×C3×D4—31no—
138C22×C3×D4—31no—
139C22×C3×D4—32no—
140C23×C3×C4—31no—
141C22×#67—32no—
142C22×#67—32no—
143C22×#67—31no—
144C22×#67—31no—
145C22×#67—32no—
146C22×#67—32no—
147C22×#67—38no—
148C22×#67—68no—
149C22×#67C2×D311yescharacteristic
150C22×#67C2×D311yescharacteristic
151C23×Dic3C2×D311yescharacteristic, complemented
152C2×D3×D4—38no—
153C2×D3×D4—38no—
154C2×D3×D4—68no—
155C2×D3×D4—68no—
156C22×D12—32no—
157C22×D12—32no—
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—38no—
161C22×D12—68no—
162C22×D12C2×D312yescomplemented
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—32no—
166C22×C4×D3—32no—
167C22×C4×D3—62no—
168C3×#123—38no—
169C3×#120—38no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C22⋊C4—21no—
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—32no—
174C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
175C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
176#953—38no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—32no—
180C2×#217—32no—
181C2×#217—61no—
182#938—316no—
183#937—38no—
184#937—316no—
185#935—38no—
186#929—38no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—32no—
190C2×(C2×D3)⋊C4—32no—
191C2×(C2×D3)⋊C4—62no—
192C2×(C2×D3)⋊C4C2×D312yescomplemented
193C2×(C2×D3)⋊C4C2×D312yescomplemented
194C2×C4⋊Dic3C2×D312yescomplemented
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197#895—316no—
198#894—316no—
199#886C2×D318yescomplemented
200#884—316no—
201#884—316no—
202#883—316no—
203#882—316no—
204#882C2×D318yescomplemented
205D3×C22⋊C4—38no—
206D3×C22⋊C4—38no—
207D3×C22⋊C4—68no—
208C23×C32—24no—
209C23×C32C2×D414yes—
210C23×C32C2412yes—
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—24no—
213C22×C3⋊D3—24no—
214C22×C3⋊D3—416no—
215C22×C3⋊D3—48no—
216C22×C3⋊D3C2×D414yes—
217C22×C3⋊D3C2×D414yes—
218C22×C3⋊D3C2×D4116yescomplemented
219C22×C3⋊D3C2412yes—
220C22×C3⋊D3C2412yes—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—24no—
224C22×C3×D3—28no—
225C22×C3×D3—24no—
226C22×C3×D3—24no—
227C22×C3×D3—24no—
228C22×C3×D3—24no—
229C22×C3×D3—48no—
230C22×C3×D3—416no—
231C22×C3×D3C2412yes—
232C22×C3×D3C2412yes—
233C22×C3×D3C2414yes—
234C2×D32—28no—
235C2×D32—48no—
236C2×D32—416no—
237C2×C32×C4—24no—
238C2×C32×C4C2414yes—
239C2×C3⋊Dic3—24no—
240C2×C3⋊Dic3C2414yes—
241C4×C3⋊D3—48no—
242C3×#67—28no—
243C3×#67—28no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—24no—
247C2×C3×Dic3—28no—
248C2×C3×Dic3C2412yes—
249C2×C3×Dic3C2414yes—
250C2×C3×Dic3C2412yes—
251C3×D12—48no—
252#626—216no—
253#626—216no—
254#626—28no—
255#626—28no—
256#625—48no—
257#624—28no—
258C23×D4—91no—
259C23×D4—91no—
260#534—916no—
261C2×#123—31no—
262C2×#123—92no—
263C2×#123—91no—
264C2×#121—92no—
265C2×#121—92no—
266C2×#120—31no—
267C2×#120—92no—
268C2×#120—91no—
269C22×C22⋊C4—91no—
270C24×C3—21no—
271C24×C3—32no—
272C24×C3—31no—
273C24×C3—31no—
274C24×C3—34no—
275C24×C3—64no—
276C24×C3—124no—
277C24×C3C22×D311yescharacteristic
278C24×C3C22×D311yescharacteristic
279C23×D3—24no—
280C23×D3—31no—
281C23×D3—31no—
282C23×D3—31no—
283C23×D3—31no—
284C23×D3—38no—
285C23×D3—38no—
286C23×D3—34no—
287C23×D3—34no—
288C23×D3—34no—
289C23×D3—34no—
290C23×D3—44no—
291C23×D3—61no—
292C23×D3—68no—
293C23×D3—64no—
294C23×D3—61no—
295C23×D3—64no—
296C23×D3—64no—
297C23×D3—124no—
298C23×D3—124no—
299C23×D3—124no—
300C23×D3—124no—
301C23×D3—128no—
302C23×D3C22×D311yescharacteristic
303C23×D3C22×D312yes—
304C23×D3C22×D311yescharacteristic
305C23×D3C22×D314yescomplemented
306C2×C3×D4—34no—
307C2×C3×D4—34no—
308C2×C3×D4—38no—
309C2×C3×D4—64no—
310C2×C3×D4—64no—
311C2×C3×D4—124no—
312C22×C3×C4—22no—
313C22×C3×C4—31no—
314C22×C3×C4—32no—
315C22×C3×C4—31no—
316C22×C3×C4—34no—
317C22×C3×C4—64no—
318C22×C3×C4C22×D312yes—
319C22×C3×C4C22×D312yes—
320C2×#67—24no—
321C2×#67—24no—
322C2×#67—38no—
323C2×#67—38no—
324C2×#67—38no—
325C2×#67—34no—
326C2×#67—38no—
327C2×#67—34no—
328C2×#67—64no—
329C2×#67—64no—
330C2×#67—68no—
331C2×#67—68no—
332C2×#67—632no—
333C2×#67—124no—
334C2×#67—124no—
335C2×#67C22×D314yes—
336C2×#67C22×D314yes—
337C22×Dic3—24no—
338C22×Dic3—32no—
339C22×Dic3—32no—
340C22×Dic3—62no—
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D312yes—
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D314yescomplemented
345D3×D4—632no—
346D3×D4—632no—
347C2×D12—38no—
348C2×D12—34no—
349C2×D12—38no—
350C2×D12—34no—
351C2×D12—44no—
352C2×D12—68no—
353C2×D12—68no—
354C2×D12—632no—
355C2×D12—64no—
356C2×D12—64no—
357C2×D12C22×D318yescomplemented
358C2×C4×D3—34no—
359C2×C4×D3—34no—
360C2×C4×D3—38no—
361C2×C4×D3—38no—
362C2×C4×D3—68no—
363C2×C4×D3—64no—
364C2×C4×D3—64no—
365C2×C4×D3—124no—
366C2×C4×D3—124no—
367C2×C4×D3—128no—
368C3×C4⋊C4—38no—
369C3×C22⋊C4—24no—
370C3×C22⋊C4—38no—
371C3×C22⋊C4—38no—
372C3×C22⋊C4C22×D314yescomplemented
373C3×C22⋊C4C22×D314yescomplemented
374#217—34no—
375#217—34no—
376#217—38no—
377#217—38no—
378#217—64no—
379(C2×D3)⋊C4—38no—
380(C2×D3)⋊C4—38no—
381(C2×D3)⋊C4—38no—
382(C2×D3)⋊C4—38no—
383(C2×D3)⋊C4—68no—
384(C2×D3)⋊C4C22×D318yescomplemented
385(C2×D3)⋊C4C22×D318yescomplemented
386C4⋊Dic3C22×D318yescomplemented
387Dic3⋊C4—38no—
388Dic3⋊C4—38no—
389C22×C32—28no—
390C22×C32—24no—
391C22×C32C22×D414yes—
392C22×C32C22×D412yes—
393C22×C32H(5,𝔽2)14yes—
394C22×C32C2511yescharacteristic
395C2×C3⋊D3—28no—
396C2×C3⋊D3—24no—
397C2×C3⋊D3—28no—
398C2×C3⋊D3—24no—
399C2×C3⋊D3—416no—
400C2×C3⋊D3C22×D414yes—
401C2×C3⋊D3C22×D414yes—
402C2×C3×D3—24no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—24no—
406C2×C3×D3—24no—
407C2×C3×D3—24no—
408C2×C3×D3—24no—
409C2×C3×D3—416no—
410C2×C3×D3—44no—
411C2×C3×D3—44no—
412C2×C3×D3—48no—
413D32—416no—
414C32×C4—24no—
415C3⋊Dic3—24no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—24no—
419C25—31no—
420C25—91no—
421C25—91no—
422C22×D4—31no—
423C22×D4—31no—
424C22×D4—32no—
425C22×D4—92no—
426C22×D4—91no—
427C22×D4—92no—
428C22×D4—91no—
429C22×D4—98no—
430C22×D4—98no—
431C22×D4—92no—
432C22×D4—188no—
433C22×D4—188no—
434C23×C4—31no—
435C23×C4—91no—
436C23×C4—92no—
437#123—38no—
438#123—916no—
439#123—98no—
440#121—916no—
441#121—916no—
442#120—38no—
443#120—916no—
444#120—98no—
445C2×C4⋊C4—32no—
446C2×C4⋊C4—92no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—92no—
450C2×C22⋊C4—92no—
451C2×C22⋊C4—91no—
452C2×C22⋊C4—92no—
453C2×C22⋊C4—98no—
454C2×C22⋊C4D3211yescharacteristic, complemented
455C23×C3—24no—
456C23×C3—24no—
457C23×C3—22no—
458C23×C3—21no—
459C23×C3—24no—
460C23×C3—32no—
461C23×C3—34no—
462C23×C3—32no—
463C23×C3—44no—
464C23×C3—68no—
465C23×C3—64no—
466C23×C3—62no—
467C23×C3—62no—
468C23×C3—64no—
469C23×C3—64no—
470C23×C3—64no—
471C23×C3—64no—
472C23×C3—128no—
473C23×C3—1216no—
474C23×C3D3×D414yes—
475C23×C3D3×D414yes—
476C23×C3C23×D312yes—
477C23×C3C23×D312yes—
478C23×C3C23×D311yescharacteristic
479C23×C3C23×D311yescharacteristic
480C22×D3—24no—
481C22×D3—28no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—24no—
485C22×D3—24no—
486C22×D3—24no—
487C22×D3—24no—
488C22×D3—34no—
489C22×D3—34no—
490C22×D3—34no—
491C22×D3—34no—
492C22×D3—32no—
493C22×D3—32no—
494C22×D3—32no—
495C22×D3—32no—
496C22×D3—316no—
497C22×D3—316no—
498C22×D3—48no—
499C22×D3—416no—
500C22×D3—64no—
501C22×D3—62no—
502C22×D3—64no—
503C22×D3—616no—
504C22×D3—62no—
505C22×D3—68no—
506C22×D3—68no—
507C22×D3—68no—
508C22×D3—64no—
509C22×D3—64no—
510C22×D3—64no—
511C22×D3—64no—
512C22×D3—124no—
513C22×D3—128no—
514C22×D3—128no—
515C22×D3—1216no—
516C22×D3—1216no—
517C22×D3—1216no—
518C22×D3—128no—
519C22×D3—128no—
520C22×D3—1216no—
521C22×D3—1216no—
522C22×D3—1232no—
523C22×D3C23×D312yes—
524C22×D3C23×D314yes—
525C22×D3C23×D312yes—
526C3×D4—68no—
527C3×D4—68no—
528C3×D4—128no—
529C2×C3×C4—24no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—32no—
533C2×C3×C4—34no—
534C2×C3×C4—32no—
535C2×C3×C4—44no—
536C2×C3×C4—62no—
537C2×C3×C4—62no—
538C2×C3×C4—68no—
539C2×C3×C4—64no—
540C2×C3×C4C23×D314yes—
541C2×C3×C4C23×D314yes—
542#67—28no—
543#67—28no—
544#67—68no—
545#67—68no—
546#67—616no—
547#67—616no—
548#67—128no—
549#67—128no—
550C2×Dic3—22no—
551C2×Dic3—22no—
552C2×Dic3—24no—
553C2×Dic3—28no—
554C2×Dic3—34no—
555C2×Dic3—34no—
556C2×Dic3—64no—
557C2×Dic3—64no—
558C2×Dic3—64no—
559C2×Dic3—124no—
560C2×Dic3C23×D312yes—
561C2×Dic3C23×D314yes—
562C2×Dic3C23×D312yes—
563D12—48no—
564D12—616no—
565D12—616no—
566D12—68no—
567D12—68no—
568C4×D3—68no—
569C4×D3—68no—
570C4×D3—128no—
571C4×D3—128no—
572C4×D3—1216no—
573C2×C32—24no—
574C2×C32#53414yescomplemented
575C2×C32C23×D411yescharacteristic
576C2×C32C2×H(5,𝔽2)12yes—
577C3⋊D3—24no—
578C3⋊D3—24no—
579C3×D3—42no—
580C3×D3—42no—
581C3×D3—44no—
582C24—31no—
583C24—32no—
584C24—31no—
585C24—34no—
586C24—64no—
587C24—94no—
588C24—91no—
589C24—91no—
590C24—94no—
591C24—98no—
592C24—124no—
593C24—184no—
594C24—364no—
595C24—364no—
596C24C2×D3211yescharacteristic
597C2×D4—34no—
598C2×D4—34no—
599C2×D4—38no—
600C2×D4—64no—
601C2×D4—64no—
602C2×D4—98no—
603C2×D4—94no—
604C2×D4—98no—
605C2×D4—94no—
606C2×D4—98no—
607C2×D4—124no—
608C2×D4—188no—
609C2×D4—188no—
610C2×D4—1832no—
611C2×D4—184no—
612C2×D4—184no—
613C2×D4—1832no—
614C2×D4—364no—
615C22×C4—34no—
616C22×C4—31no—
617C22×C4—32no—
618C22×C4—31no—
619C22×C4—64no—
620C22×C4—94no—
621C22×C4—92no—
622C22×C4—98no—
623C22×C4—184no—
624C22×C4—364no—
625C22×C4C2×D3212yes—
626C4⋊C4—38no—
627C4⋊C4—98no—
628C22⋊C4—38no—
629C22⋊C4—38no—
630C22⋊C4—98no—
631C22⋊C4—98no—
632C22⋊C4—94no—
633C22⋊C4—98no—
634C22⋊C4C2×D3214yescomplemented
635C22×C3—28no—
636C22×C3—24no—
637C22×C3—24no—
638C22×C3—28no—
639C22×C3—22no—
640C22×C3—24no—
641C22×C3—24no—
642C22×C3—21no—
643C22×C3—44no—
644C22×C3—48no—
645C22×C3—64no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—64no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—1216no—
653C22×C3—124no—
654C22×C3—128no—
655C22×C3—124no—
656C22×C3C2×D3×D414yes—
657C22×C3C2×D3×D414yes—
658C22×C3C2×D3×D412yes—
659C22×C3C2×D3×D412yes—
660C22×C3#100414yes—
661C22×C3#100914yes—
662C22×C3C24×D311yescharacteristic
663C22×C3C24×D311yescharacteristic
664C2×D3—24no—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—24no—
668C2×D3—24no—
669C2×D3—24no—
670C2×D3—24no—
671C2×D3—34no—
672C2×D3—34no—
673C2×D3—34no—
674C2×D3—34no—
675C2×D3—416no—
676C2×D3—44no—
677C2×D3—48no—
678C2×D3—44no—
679C2×D3—64no—
680C2×D3—64no—
681C2×D3—68no—
682C2×D3—616no—
683C2×D3—68no—
684C2×D3—68no—
685C2×D3—64no—
686C2×D3—64no—
687C2×D3—64no—
688C2×D3—64no—
689C2×D3—68no—
690C2×D3—68no—
691C2×D3—124no—
692C2×D3—128no—
693C2×D3—1216no—
694C2×D3—1216no—
695C2×D3—1216no—
696C2×D3—1216no—
697C2×D3—1232no—
698C3×C4—24no—
699C3×C4—24no—
700C3×C4—44no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—64no—
704Dic3—22no—
705Dic3—22no—
706Dic3—24no—
707Dic3—64no—
708Dic3—64no—
709Dic3—124no—
710C32C2×#53411yescharacteristic, complemented, Sylow
711C23—24no—
712C23—32no—
713C23—34no—
714C23—32no—
715C23—62no—
716C23—62no—
717C23—68no—
718C23—64no—
719C23—64no—
720C23—64no—
721C23—64no—
722C23—64no—
723C23—94no—
724C23—94no—
725C23—92no—
726C23—92no—
727C23—916no—
728C23—128no—
729C23—1216no—
730C23—188no—
731C23—184no—
732C23—184no—
733C23—368no—
734C23—3616no—
735C23—368no—
736C23—3616no—
737C23#380214yes—
738C23C22×D3212yes—
739C23C22×D3211yescharacteristic
740D4—68no—
741D4—68no—
742D4—128no—
743D4—1816no—
744D4—1816no—
745D4—188no—
746D4—188no—
747D4—368no—
748C2×C4—24no—
749C2×C4—32no—
750C2×C4—34no—
751C2×C4—32no—
752C2×C4—68no—
753C2×C4—64no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—94no—
757C2×C4—188no—
758C2×C4—184no—
759C2×C4—368no—
760C2×C4C22×D3214yes—
761C2×C3—24no—
762C2×C3—24no—
763C2×C3—21no—
764C2×C3—22no—
765C2×C3—24no—
766C2×C3—44no—
767C2×C3—122no—
768C2×C3—122no—
769C2×C3—124no—
770C2×C3#558914yescomplemented
771C2×C3#565314yescomplemented
772C2×C3C22×D3×D411yescharacteristic
773C2×C3C22×D3×D411yescharacteristic
774C2×C3C2×#100412yes—
775C2×C3C2×#100912yes—
776D3—44no—
777D3—42no—
778D3—42no—
779D3—68no—
780D3—64no—
781D3—64no—
782D3—64no—
783D3—64no—
784D3—124no—
785C22—24no—
786C22—28no—
787C22—62no—
788C22—62no—
789C22—64no—
790C22—64no—
791C22—64no—
792C22—64no—
793C22—64no—
794C22—94no—
795C22—94no—
796C22—1216no—
797C22—128no—
798C22—124no—
799C22—124no—
800C22—184no—
801C22—184no—
802C22—188no—
803C22—188no—
804C22—3616no—
805C22—3616no—
806C22C2×#380214yes—
807C22C2×#380212yes—
808C22#6431414yes—
809C22C23×D3211yescharacteristic
810C4—24no—
811C4—64no—
812C4—62no—
813C4—62no—
814C4—184no—
815C3—21no—
816C3C2×#558911yescharacteristic, complemented
817C3C2×#565311yescharacteristic, complemented
818C2—24no—
819C2—124no—
820C2—122no—
821C2—122no—
822C2—184no—
823C2—184no—
824C2#1059429614yesdirect product factor
825C2C22×#380211yescharacteristic
826C2C2×#6431412yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#3811C2semidirect
2. C23×#626C2semidirect
3. C2×C22⋊C4×C3⋊D3C2semidirect
4. C2×C3×#886C2semidirect
5. C2×C3×#882C2semidirect
6. C2×#63976C2semidirect
7. C2×#63961C2semidirect
8. C2×#63922C2semidirect
9. C2×#63916C2semidirect
10. C2×#63912C2semidirect
11. C2×#63854C2semidirect
12. #10594296C2direct (N × H)
16. C24×C3×D3C22semidirect
17. C23×D32C22semidirect
18. C22×C4×C3⋊D3C22semidirect
21. C23×C3×Dic3C22semidirect
22. C22×C3×D12C22semidirect
24. C2×#3811C22semidirect
27. C22×#626C22semidirect
28. C22×#626C22semidirect
29. C22×#626C22semidirect
30. C22×#626C22semidirect
31. C22×#625C22semidirect
32. C22×#624C22semidirect
33. C2×C32×C22⋊C4C22semidirect
34. C2×#3757C22semidirect
35. C2×#3752C22semidirect
36. C22⋊C4×C3⋊D3C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C3×#886C22semidirect
41. C3×#882C22semidirect
42. #63976C22semidirect
43. C2×#3724C22semidirect
44. #63961C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. #63922C22semidirect
48. #63916C22semidirect
49. #63912C22semidirect
50. #63854C22semidirect
67. C2×#886D3semidirect
72. C2×#882D3semidirect
78. C23×C3⋊D3D4semidirect
87. C23×C3×D3C23semidirect
90. C22×D32C23semidirect
94. C2×C4×C3⋊D3C23semidirect
103. C22×C3×Dic3C23semidirect
105. C2×C3×D12C23semidirect
113. C2×#626C23semidirect
114. C2×#626C23semidirect
115. C2×#626C23semidirect
117. C2×#625C23semidirect
119. C2×#624C23semidirect
120. C32×C22⋊C4C23semidirect
121. #3757C23semidirect
122. #3752C23semidirect
123. C3×(C2×D3)⋊C4C23semidirect
124. C3×(C2×D3)⋊C4C23semidirect
125. C3×C4⋊Dic3C23semidirect
126. #3724C23semidirect
127. (C2×D3)⋊Dic3C23semidirect
128. (C2×D3)⋊Dic3C23semidirect
136. C24×D3C2×D3semidirect
151. C23×Dic3C2×D3semidirect
162. C22×D12C2×D3semidirect
174. C2×C3×C22⋊C4C2×D3semidirect
175. C2×C3×C22⋊C4C2×D3semidirect
192. C2×(C2×D3)⋊C4C2×D3semidirect
193. C2×(C2×D3)⋊C4C2×D3semidirect
194. C2×C4⋊Dic3C2×D3semidirect
199. #886C2×D3semidirect
204. #882C2×D3semidirect
218. C22×C3⋊D3C2×D4semidirect
305. C23×D3C22×D3semidirect
344. C22×Dic3C22×D3semidirect
357. C2×D12C22×D3semidirect
372. C3×C22⋊C4C22×D3semidirect
373. C3×C22⋊C4C22×D3semidirect
384. (C2×D3)⋊C4C22×D3semidirect
385. (C2×D3)⋊C4C22×D3semidirect
386. C4⋊Dic3C22×D3semidirect
454. C2×C22⋊C4D32semidirect
574. C2×C32#534semidirect
634. C22⋊C4C2×D32semidirect
710. C32C2×#534semidirect
770. C2×C3#5589semidirect
771. C2×C3#5653semidirect
816. C3C2×#5589semidirect
817. C3C2×#5653semidirect
824. C2#10594296direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#38112
C23×#6262
C2×C22⋊C4×C3⋊D32
C2×C3×#8862
C2×C3×#8822
C2×#639762
C2×#639612
C2×#639222
C2×#639162
C2×#639122
C2×#638542
#105942962
C2×#56533
C2×#55893